Chapter 11.2, Problem 45E

Let r(t) (15, cos t, -3 sin t) be the position vector of an object. Find the velocity and speed of the object.

A bee fles around a room at an altitude of 2= 2.3 meters making circles, so that its r coordinate varies from 1.3 to 1.9 meters, and its y coordinate varies from 2.2 to 2.8 meters. The bee completes one circle every 2.3 seconds. At sime=0 seconds, the bee's y coordinate is 2.8 meters and its velocity vector is completely in the +i direction. Write parametric equations to describe the motion of the bee z(t)= sin(2p/23)+22 y(t) =30(2pit2:3)+1.9 z(t) = 23

A particle moves in space along a path whose parametric equations are given by x1 = b sin(wt), x2 = b cos(wt), x3 = c where b and c are constants. a. Find its position at vector 7, velocity v, and acceleration å at any time t. b. Show that the particle traverses its path with constant speed and that its distance from the origin remains constant. c. Show that the acceleration is perpendicular to the velocity and the x3-axis. d. Determine the trajectory of the particle, that is, the path described in terms of spatial coordinates only. Sketch the trajectory. 1.